reserve i,j,k,n,m for Nat;
reserve p,q for Point of TOP-REAL 2;
reserve G for Go-board;
reserve C for Subset of TOP-REAL 2;

theorem
  for f being non constant standard special_circular_sequence, g being
  FinSequence of TOP-REAL2 holds g is_in_the_area_of f iff g is_in_the_area_of
  SpStSeq L~f
proof
  let f be non constant standard special_circular_sequence, g be FinSequence
  of TOP-REAL2;
A1: S-bound L~SpStSeq L~f = S-bound L~f by SPRECT_1:59;
A2: N-bound L~SpStSeq L~f = N-bound L~f by SPRECT_1:60;
A3: E-bound L~SpStSeq L~f = E-bound L~f by SPRECT_1:61;
A4: W-bound L~SpStSeq L~f = W-bound L~f by SPRECT_1:58;
  thus g is_in_the_area_of f implies g is_in_the_area_of SpStSeq L~f
  by A4,A1,A2,A3;
  assume
A5: g is_in_the_area_of SpStSeq L~f;
  let n;
  thus thesis by A4,A1,A2,A3,A5;
end;
